Predicting Plant Extinctions with Random Forests

Kristen Monaco, Praya Cheekapara, Raymond Fleming, Teng Ma

Introduction and Lit Review

Introduction

Ensemble machine learning method based on a large number of decision trees voting to predict a classification
Benefits compared to decision tree:
- Able to function with incomplete data
- Lower likelihood of an overfit
- Improved prediction accuracy

Random Forest Applications

Regression
- Price Prediction
- Demand Forecasting
- Time-series Analysis
Remote Sensing
- Vegetation Mapping
- Environmental Monitoring

Bioinformatics
- Disease Diagnosis
- Protein Classification
- Gene Expression
Banking and Business
- Fraud Detection
- Targeted Marketing

Literature Review

Feature Selection can be performed by training a large, unpruned random forest then feature importance can be used to help with identifying the most important features [@jaiswal2017application], leading to a reduction in computational requirements for a similar result as demonstrated in selecting features for human activity recognition [@uddin2015guided]
- This method can be used to select features for a Random Forest but could also be used to assist in feature selection for other models as well

Methods

Bagging
Boosting
Random Feature Selection
Cross Validation

Random Forest Improvements

Bootstrap Sampling (Bagging)
- Each decision tree uses a random sample of the original dataset
  - Using a subset of the dataset reduces the probability of an overfit model
  - Rows with missing data will often be left out of the sample, improving performance
  - Performed with replacement
Boosting
- When individual models are trained in a sequential way, each model then learns the mistakes made by the preceding model.

Random Forest Improvements Continued

A random set of features is selected for each node in training
- Information about feature importance may be saved and applies in future iterations
- Even with automated random feature selection, feature selection and engineering prior to training may improve performance

Decision Tree

Single decision trees may be visualized to help modelers understand the dataset
- Important features for a single decision tree will likely be important for a full model

Decision Tree Visualization Code

 m3 <- rpart(
   formula = Group~ LF + GF + Biomes + Range +
     Habitat_degradation + Habitat_loss + IAS +
     Other + Unknown + Other + Over_exploitation,
   data    = species_train,
   method  = "anova"
 )
 rpart.plot(m3)

Validation Metrics

Validation of performance of model
- Resampling method similar to out of bag estimation
- Allows estimation of the general performance of a model

Data

South African Red List
- Data about plants with their habitat, traits, distribution, and factors influencing their current threatened/extinct status
Purpose
- Predict whether or not an unknown plant is extinct based on the above characteristics

Distribution of Range by Conservation Status

While there are a small number of threatened species with a large range, it is clear that Range is likely a strong predictor of Group status
A lower range predicts a higher likelihood of threatened or extinct grouping.

Distribution Visualization Code

ggplot(data = data, aes(x = Status, y = Range, fill = Status)) +
  geom_boxplot() +
  theme_bw() +
  ylim(0,100000)

Feature Associations

Cramer’s V Association with Range binned into 20 categories
- Target feature Group is most associated with Range, Family, Habitat Loss, Biome, and GF
- The most associated features will likely be the most important training features
- Colinearity does not appear to be present

Association Visualization Code

corrDF <- train %>% mutate(Range=ntile(Range, n=20))
corrDF <- 
corrDF <- corrDF %>% select(!GenSpec) %>% mutate(across(c("Group","LF","GF","Range",
                                     "Biomes","Range","Habitat_degradation",
                                     "Habitat_loss","IAS","Other",
                                     "Over_exploitation","Pollution","Unknown"),
                                     as_factor))

ggcorrplot::ggcorrplot(DescTools::PairApply(corrDF,DescTools::CramerV), type='lower')

Analysis and Results

Data Preparation

Preprocessing
- Encode categorical features into numerical / factor features
- Split the training set into a training and test set,
- Minimize class imbalance

Data Split Code

features <- data[, 1:14]
label <- data[, 15]

split <- sample.split(label, SplitRatio = 0.7)
features_train = features[split,]
features_test = features[!split,]
label_train = label[split]
label_test = label[!split]

data_train <- features_train
data_train$label <- label_train

  Raw       Factor
1 Parasitic 1     
2 Tree      2     
3 Suffrutex 3

Factorization Table Code

corrDF <- train %>% 
            mutate(Range=ntile(Range, n=20))

corrDF <- corrDF %>% 
            mutate(across(c(
              "Group","LF","GF","Range",
              "Biomes","Range",
              "Habitat_degradation",
              "Habitat_loss", "IAS","Other",
              "Over_exploitation","Pollution",
              "Unknown"),as_factor))

printFactors=matrix(
              c(train$GF[1],train$GF[2],
                train$GF[3],corrDF$GF[1],
                corrDF$GF[2],corrDF$GF[3]),
                nrow=3)

colnames(printFactors)=c('Raw','Factor')
rownames(printFactors)=c('1','2','3')
print(printFactors,quote=FALSE)

Class Balancing

Class Imbalance
- Resample smaller classes in order to approximate equal classes
- Training on imbalanced datasets will bias predictions to the larger class

Group Counts Pre-Balancing:   490 148 23 
Group Counts Post-Balancing:  490 490 490

Class Balancing Code

AB <- data_train
AB <- AB[AB$label != '3',]
AB_res <- ovun.sample(label ~ ., data = AB, 
                      method = "over", N = 980,
                      seed = 1)$data

AC <- data_train
AC <- AC[AC$label != '2',]
AC_res <- ovun.sample(label ~ ., data = AC,
                      method = "over", N = 980,
                      seed = 1)$data

AB_2 <- AB_res[AB_res$label == '2',]
AC_3 <- AC_res[AC_res$label == '3',]

data_train_1 <- AB_res[AB_res$label == '1',]
data_train_combined <- rbind(data_train_1, AB_2, AC_3)

cat("Group Counts Pre-Balancing:  ", 
    table(data_train$label),
    "\nGroup Counts Post-Balancing: ", 
    table(data_train_combined$label))

\(X_{new}=\frac{X_{old}-\min(X_{old})}{\max(X_{old})-\min(x_{old})}\)

          Score
Accuracy   0.93
Recall     0.87
Precision  0.89
F1         0.88

Min-Max Normalization maps features into the range of 0 to 1
- The largest value scales to 1
- The smallest scales to zero
- Features on the same scale will often predict with a higher reliability

MinMax Code

trainMM <- as.data.frame(lapply(features_train, 
                      function(x) {(x-min(x))/(max(x)-min(x))}))
testMM <- as.data.frame(lapply(features_test, 
                      function(x) {(x-min(x))/(max(x)-min(x))}))

train <- trainMM
train$label <- label
MMCounts <- table(train$label)

MM <- randomForest(x = train[-ncol(data_train_combined)],
                        y = as.factor(train$label), ntree = 2)
importanceMM = importance(MM)
PredMM <- predict(MM, testMM)
accuracy <- sum(label_test == PredMM) / length(label_test)
testfactorMM <- as.factor(label_test)
PredFactorMM <- as.factor(PredMM)
cm <- confusionMatrix(PredFactorMM, testfactorMM)
rownames(cm$byClass)<-c("LC","Thr","Ext")
recall <- mean(c(cm$byClass["LC", "Sensitivity"], 
                 cm$byClass["Thr", "Sensitivity"], 
                 cm$byClass["Ext", "Sensitivity"]))
precision <- mean(c(cm$byClass["LC", "Pos Pred Value"], 
                    cm$byClass["Thr", "Pos Pred Value"], 
                    cm$byClass["Ext", "Pos Pred Value"]))
F1 = 2 * recall * precision / ( recall + precision )
printTable=matrix(c(round(accuracy,2),round(recall,2),
                    round(precision,2),round(F1,2)),
                  ncol=1,byrow=TRUE)
colnames(printTable)=c('Score')
rownames(printTable)=c('Accuracy','Recall',
                       'Precision','F1')
print(printTable)

\(X_{new}=\frac{X_{old}-\bar{X}_{old}}{\sigma_{X_{old}}}\)

          Score
Accuracy   0.33
Recall     0.40
Precision  0.31
F1         0.35

Z-Score Scaling scales features to have a mean of zero and standard deviation of 1
- In this dataset, Range has a much different range between the 3 groups
- This type of normalization reduces the effect of the difference on the model

ZScore Code

TrainZS <- as.data.frame(lapply(features_train, 
                      function(x) {(x - mean(x))/sd(x)}))
TestZS <- as.data.frame(lapply(features_test, 
                      function(x) {(x - mean(x))/sd(x)}))

train <- TrainZS
train$label <- label
ZSCounts <- table(train$label)

ZS <- randomForest(x = train[-ncol(data_train_combined)],
                      y = as.factor(train$label), ntree = 2)
ImportanceZS = importance(ZS)
PredZS <- predict(ZS, TestZS)
accuracy <- sum(label_test == PredZS) / length(label_test)
label_test_factor <- as.factor(label_test)
PredFactorZS <- as.factor(PredZS)
cm <- confusionMatrix(PredFactorZS, label_test_factor)
recall <- mean(c(cm$byClass["Class: 1", "Sensitivity"],
                              cm$byClass["Class: 2", "Sensitivity"],
                              cm$byClass["Class: 3", "Sensitivity"]))

precision <- mean(c(cm$byClass["Class: 1", "Pos Pred Value"],
                            cm$byClass["Class: 2", "Pos Pred Value"],
                            cm$byClass["Class: 3", "Pos Pred Value"]))
F1 = 2 * recall * precision / ( recall + precision )
printTable=matrix(c(round(accuracy,2),round(recall,2),
                    round(precision,2),round(F1,2)),
                  ncol=1,byrow=TRUE)
colnames(printTable)=c('Score')
rownames(printTable)=c('Accuracy','Recall','Precision','F1')
print(printTable)

\(X_{new}=\frac{X_{old}}{\max(|X_{old}|)}\)

          Score
Accuracy   0.88
Recall     0.80
Precision  0.79
F1         0.79

Max Absolute Value Normalization is a special case of Min-Max Normalization
- If all values are positive, normalization is simply a ratio of value to max value
- May only be used if all values for the feature are positive

Max Absolute Value Code

TrainMAV <- as.data.frame(lapply(features_train, 
                       function(x) {x / max(abs(x))}))
TestMAV <- as.data.frame(lapply(features_test, 
                        function(x) {x / max(abs(x))}))

train <- TrainMAV
train$label <- label
MAVCounts <- table(train$label)

MAV <- randomForest(x = train[-ncol(data_train_combined)], 
                        y = as.factor(train$label), 
                        ntree = 2)
ImportanceMAV = importance(MAV)
PredMAV <- predict(MAV, TestMAV)
accuracy <- sum(label_test == PredMAV) / length(label_test)
label_test_factor <- as.factor(label_test)
PredFactorMAV <- as.factor(PredMAV)
cm <- confusionMatrix(PredFactorMAV, label_test_factor)
recall <- mean(c(cm$byClass["Class: 1", "Sensitivity"],
                 cm$byClass["Class: 2", "Sensitivity"],
                 cm$byClass["Class: 3", "Sensitivity"]))
precision <- mean(c(cm$byClass["Class: 1", "Pos Pred Value"],
                 cm$byClass["Class: 2", "Pos Pred Value"],
                 cm$byClass["Class: 3", "Pos Pred Value"]))
F1 = 2 * recall * precision / ( recall + precision )
printTable=matrix(c(round(accuracy,2),round(recall,2),
                    round(precision,2),round(F1,2)),
                  ncol=1,byrow=TRUE)
colnames(printTable)=c('Score')
rownames(printTable)=c('Accuracy','Recall','Precision','F1')
print(printTable)

\(X_{new}=\frac{X_{old}}{\sum(|X_{old}|)}\)

          Score
Accuracy   0.77
Recall     0.60
Precision  0.55
F1         0.57

L1 Normalization is similar to Max Absolute Value Normalization
- Rather than a ratio of current value to Max Absolute Value, L1 normalization is a ratio of current value to the sum of absolute values.
- When complete, the sum of absolute values will equal 1

L1 Code

trainL1 <- as.data.frame(lapply(features_train, 
                       function(x) {x / sum(abs(x))}))
TestL1 <- as.data.frame(lapply(features_test, 
                       function(x) {x / sum(abs(x))}))

train <- trainL1
train$label <- label
L1Counts <- table(train$label)

L1 <- randomForest(x = train[-ncol(data_train_combined)], 
                        y = as.factor(train$label), ntree = 2)
L1Importance = importance(L1)
PredL1 <- predict(L1, TestL1)
accuracy <- sum(label_test == PredL1) / length(label_test)
label_test_factor <- as.factor(label_test)
PredFactorL1 <- as.factor(PredL1)
cm <- confusionMatrix(PredFactorL1, label_test_factor)
recall <- mean(c(cm$byClass["Class: 1", "Sensitivity"],
                              cm$byClass["Class: 2", "Sensitivity"],
                              cm$byClass["Class: 3", "Sensitivity"]))
precision <- mean(c(cm$byClass["Class: 1", "Pos Pred Value"],
                            cm$byClass["Class: 2", "Pos Pred Value"],
                            cm$byClass["Class: 3", "Pos Pred Value"]))
F1 = 2 * recall * precision / ( recall + precision )
printTable=matrix(c(round(accuracy,2),round(recall,2),
                    round(precision,2),round(F1,2)),
                    ncol=1,byrow=TRUE)
colnames(printTable)=c('Score')
rownames(printTable)=c('Accuracy','Recall','Precision','F1')
print(printTable)

\(X_{new}=\frac{X_{old}}{\sqrt{\sum{X_{old}^2}}}\)

          Score
Accuracy   0.75
Recall     0.62
Precision  0.53
F1         0.57

L2 Normalization is based on distance from current value to the origin
- Ratio of current value to the distance from the current value to the origin
- Outliers have a stronger effect with L2 normalization

L2 Code

TrainL2 <- as.data.frame(lapply(features_train, 
                       function(x) {x / sqrt(sum(x^2))}))
TestL2 <- as.data.frame(lapply(features_test, 
                       function(x) {x / sqrt(sum(x^2))}))

train <- TrainL2
train$label <- label
L2Counts <- table(train$label)

L2 <- randomForest(x = train[-ncol(data_train_combined)], 
                        y = as.factor(train$label), ntree = 2)
L2Importance = importance(L2)
PredL2 <- predict(L2, TestL2)
accuracy <- sum(label_test == PredL2) / length(label_test)
label_test_factor <- as.factor(label_test)
PredFactorL2 <- as.factor(PredL2)
cm <- confusionMatrix(PredFactorL2, label_test_factor)

recall <- mean(c(cm$byClass["Class: 1", "Sensitivity"],
                 cm$byClass["Class: 2", "Sensitivity"],
                 cm$byClass["Class: 3", "Sensitivity"]))

precision <- mean(c(cm$byClass["Class: 1", "Pos Pred Value"],
                 cm$byClass["Class: 2", "Pos Pred Value"],
                 cm$byClass["Class: 3", "Pos Pred Value"]))

F1 = 2 * recall * precision / ( recall + precision )

printTable=matrix(c(round(accuracy,2),round(recall,2),
                    round(precision,2),round(F1,2)),ncol=1,
                    byrow=TRUE)
colnames(printTable)=c('Score')
rownames(printTable)=c('Accuracy','Recall','Precision','F1')

print(printTable)

Prediction Method

Each independently trained decision tree produces its own prediction
- Trained on different subsets of both data and features
The results from each decision tree are combined into a voting classifier using a Mode function
- \(y_{final}=\text{mode}(\{y_1,y_2,y_3,y_4,y_5\})\)
Iterate over entire test set, storing results
Generate a confusion matrix, calculate the sensitivity, and precision for each category

Prediction

          Score
Accuracy   0.90
Recall     0.82
Precision  0.76
F1         0.79

Prediction using a combination of trees leads to a better accuracy on all metrics

Prediction Code

n <- length(PredMM)
final_pred <-rep(NA, n)
for(i in 1:n) {
   preds <- c(PredMM[i], PredZS[i], PredMAV[i], 
              PredL1[i], PredL2[i])
   final_pred[i] <-as.numeric(names(which.max(table(preds))))
}

accuracy <-sum(label_test == final_pred)/length(label_test)

final_pred_factor <-as.factor(final_pred)
label_test_factor <-as.factor(label_test)
cm_vote <-confusionMatrix(final_pred_factor, label_test_factor)
rownames(cm_vote$byClass)<-c("LC","Thr","Ext")
sensitivity_class1 <-cm_vote$byClass["LC", "Sensitivity"]
sensitivity_class2 <-cm_vote$byClass["Thr", "Sensitivity"]
sensitivity_class3 <-cm_vote$byClass["Ext", "Sensitivity"]
recall =(sensitivity_class1+sensitivity_class2+sensitivity_class3)/3

precision_class1 <-cm_vote$byClass["LC", "Pos Pred Value"]
precision_class2 <-cm_vote$byClass["Thr", "Pos Pred Value"]
precision_class3 <-cm_vote$byClass["Ext", "Pos Pred Value"]
precision=(precision_class1+precision_class2+precision_class3)/3

F1=2*recall*precision/(recall+precision)

Table Print Code

printTable=matrix(c(round(accuracy,2),round(recall,2),
                    round(precision,2),round(F1,2)),ncol=1,
                    byrow=TRUE)
colnames(printTable)=c('Score')
rownames(printTable)=c('Accuracy','Recall','Precision','F1')
print(printTable)

Feature Importance

Range is the most important feature to predict Group Status
- Habitat Loss and Growth Form are also important features
- Life Form, Other, and Unknown are unimportant for prediction

Feature Importance Visualization Code

ctrl <- trainControl(method = "cv",  
                     number = 10) 

bagged_cv <- train(
  Group~ LF + GF + Biomes + Range +
    Habitat_degradation + 
    Habitat_loss + IAS + Other +
    Unknown + Other +
    Over_exploitation,
  data    = species_train,
  method = "treebag",
  trControl = ctrl,
  importance = TRUE
)
 
plot(varImp(bagged_cv), 10)

Evaluation

\(\text{Accuracy}\)

\(\text{Recall}\)

\(\text{Precision}\)

\(\text{F1}\)

\(=\frac{\sum{\left(\text{Actual Label} = \text{Predicted Label}\right)}}{\text{Label Count}}\)

\(=\frac{\text{True Positives}}{\text{True Positives} + \text{False Negatives}}\)

\(=\frac{\text{True Positives}}{\text{True Positives}+\text{False Positives}}\)

\(=\frac{2*(\text{Precision}*\text{Recall})}{\text{Precision}+\text{Recall}}\)

          Score
Accuracy   0.90
Recall     0.82
Precision  0.76
F1         0.79

Evaluation Metrics Code

n <- length(PredMM)
final_pred <-rep(NA, n)
for(i in 1:n) {
   preds <- c(PredMM[i], PredZS[i], PredMAV[i],
              PredL1[i], PredL2[i])
   final_pred[i] <-as.numeric(names(
                    which.max(table(preds))))
}

accuracy <-sum(label_test == final_pred)/
            length(label_test)

final_pred_factor<-as.factor(final_pred)
label_test_factor<-as.factor(label_test)
cm_vote <-confusionMatrix(final_pred_factor,
                          label_test_factor)
rownames(cm_vote$byClass)<-c("LC","Thr","Ext")
sensitivity_class1<-cm_vote$byClass[
                    "LC", "Sensitivity"]
sensitivity_class2<-cm_vote$byClass[
                    "Thr", "Sensitivity"]
sensitivity_class3<-cm_vote$byClass[
                    "Ext",  "Sensitivity"]
recall =(sensitivity_class1+sensitivity_class2+
           sensitivity_class3)/3

precision_class1<-cm_vote$byClass[
                  "LC",  "Pos Pred Value"]
precision_class2<-cm_vote$byClass[
                  "Thr",  "Pos Pred Value"]
precision_class3<-cm_vote$byClass[
                  "Ext", "Pos Pred Value"]
precision=(precision_class1+precision_class2+
             precision_class3)/3

F1=2*recall*precision/(recall+precision)

printTable=matrix(c(round(accuracy,2),
                    round(recall,2),
                    round(precision,2),
                    round(F1,2)),ncol=1,
                    byrow=TRUE)
colnames(printTable)=c('Score')
rownames(printTable)=c('Accuracy','Recall',
                       'Precision','F1')
print(printTable)

Confusion Matrix and Statistics

                 Score      
Accuracy         0.9        
Accuracy p-value <.001      
95% CI           (0.86,0.93)
Kappa            0.75

                       LC  Thr  Ext
Sensitivity          0.97 0.68 0.80
Specificity          0.84 0.97 0.97
Pos Pred Value       0.94 0.86 0.47
Neg Pred Value       0.91 0.91 0.99
Precision            0.94 0.86 0.47
Recall               0.97 0.68 0.80
F1                   0.96 0.76 0.59
Prevalence           0.74 0.22 0.04
Detection Rate       0.72 0.15 0.03
Detection Prevalence 0.76 0.18 0.06
Balanced Accuracy    0.90 0.83 0.88

Confusion Matrix Code

cm_vote <- confusionMatrix(final_pred_factor, label_test_factor)
cm <- confusionMatrix(final_pred_factor, label_test_factor)

cm_d <- as.data.frame(cm$table)
cm_st <-data.frame(cm$overall)
cm_st$cm.overall <- round(cm_st$cm.overall,2)
cm_d$diag <- cm_d$Prediction == cm_d$Reference
cm_d$ndiag <- cm_d$Prediction != cm_d$Reference     
cm_d[cm_d == 0] <- NA
cm_d$Reference <-  reverse.levels(cm_d$Reference)
cm_d$ref_freq <- cm_d$Freq * ifelse(is.na(cm_d$diag),-1,1) 
 
plt1 <-  ggplot(data = cm_d, aes(x = Prediction , y =  Reference, 
                                 fill = Freq))+
  scale_x_discrete(position = "top") +
  geom_tile( data = cm_d,aes(fill = ref_freq)) +
  scale_fill_gradient2(guide = FALSE ,low="red",high="mediumvioletred", 
                       mid= "mistyrose",
                    midpoint = 0,na.value = 'white') +
  geom_text(aes(label = Freq), color = 'black', size = 3)+
  theme_bw() +
  theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
        legend.position = "none",
        panel.border = element_blank(),
        plot.background = element_blank(),
        axis.line = element_blank(),
  )
plt2 <-  tableGrob(cm_st)
grid.arrange(plt1, plt2, nrow = 1, ncol = 2,
            top=textGrob("Confusion Matrix",gp=gpar(fontsize=25,font=1)))

Table Print Code

printTable=matrix(c(round(cm$overall['Accuracy'],2),
                    if(cm$overall['AccuracyPValue']<0.001){"<.001"}
                    else round(cm$overall['AccuracyPValue'],3),
                    paste("(",round(cm$overall['AccuracyLower'],2),
                          ",",round(cm$overall['AccuracyUpper'],2),
                          ")",sep=""),
                    round(cm$overall['Kappa'],2)),ncol=1,
                    byrow=TRUE)
colnames(printTable)=c('Score')
rownames(printTable)=c('Accuracy','Accuracy p-value','95% CI','Kappa')
print(printTable,quote=FALSE)

cmBC<-cm$byClass
rownames(cmBC)<-c("LC","Thr","Ext")
print(t(round(cmBC,2)),quote=FALSE)

Conclusion

Predictive Model with 88% Accuracy.
Range was the strongest predictor of extinction.
- Cape Floristic region (Fynbos biome)
- Perennial shrubs
Habitat loss was the 2nd most important variable.
Further studies could include increased surveillance of threats, species monitoring, and ecological value of plant biodiversity.